How do you evaluate the accuracy of a time series model?

To evaluate the accuracy of a time series model, you need to use metrics that quantify prediction errors, validate the model’s stability over time, and assess its practical relevance. Common metrics include Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE). These metrics measure the average deviation between predicted and actual values, but each emphasizes different aspects of error. For example, RMSE penalizes larger errors more heavily than MAE, making it useful for highlighting significant outliers. MAPE expresses errors as percentages, which helps when comparing performance across datasets with varying scales. It’s also critical to use time-aware cross-validation, such as rolling windows or expanding windows, to ensure the model generalizes well to unseen data without leaking future information into training.

Beyond metrics, visualizing predictions against actual data is a practical way to identify patterns the model might miss. For instance, plotting the forecast alongside historical data can reveal whether the model captures seasonality, trends, or sudden shifts (e.g., a spike in sales during holidays). Residual analysis—checking if prediction errors are random and evenly distributed—is another key step. If residuals show autocorrelation (e.g., errors consistently increasing over time), the model may not account for underlying patterns. Tools like autocorrelation function (ACF) plots or Ljung-Box tests help detect these issues. For example, a retail demand forecasting model with seasonal residuals might need stronger seasonal decomposition or external regressors for holidays.

Finally, consider domain-specific requirements. A stock price prediction model might prioritize directional accuracy (predicting upward or downward movement) over absolute error, while an energy demand model could focus on minimizing peak-hour errors. Testing robustness across multiple time periods is also essential. For example, a model trained on pre-pandemic data should be validated against pandemic-era data to check adaptability. Walk-forward validation, where the model is retrained incrementally and tested on the next time window, simulates real-world deployment. Combining quantitative metrics, visual checks, and domain context ensures a comprehensive evaluation that balances statistical rigor with practical utility.